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Backlund transformations for discrete Painleve´ equations: Discrete PII–PV
Sakka, Ayman H.; Mugan, Ugurhan (2006)Transformation properties of discrete Painleve´ equations are investigated by using an algorithmic method. This method yields explicit transformations which relates the solutions of discrete Painleve´ equations, discrete ... 
Bäcklund Transformations for Fifthorder Painlevé Equations
Sakka, Ayman H. (Walter de Gruyter GmbH, 20051001)In this article we study B¨acklund transformations of the fifthorder Painlev´e equations FifI, FifII, FifIII and FifIV. We derive B¨acklund transformations between these equations and new fifthorder Painlev´e ... 
Bäcklund transformations for fifth–order Cosgrove’s equations
Sakka, Ayman H.; Elshamy, Safejan R. (الجامعة الإسلامية  غزة, 2007)In this article we use a generalization of Fokas and Ablowitz algorithm to obtain Baecklund transformations (BTs) for the fifthorder ordinary differential equations of Cosgrove, FifFifII, FifIII, and FifIV. We derive ... 
Bäcklund Transformations for First and Second Painlevé Hierarchies
Sakka, Ayman H. (SIGMA (Symmetry, Integrability and Geometry: Methods and Application), 20090302)We give B¨acklund transformations for first and second Painlev´e hierarchies. These B¨acklund transformations are generalization of known B¨acklund transformations of the first and second Painlev´e equations and they ... 
Bäcklund transformations for higher order Painlevé equations
Gordoa, P.R.; Muğan, U.; Pickering, A.; Sakka, A. (Elsevier BV, 200412)We present a new generalized algorithm which allows the construction of Bäcklund transformations (BTs) for higher order ordinary differential equations (ODEs). This algorithm is based on the idea of seeking transformations ... 
Bäcklund transformations for Painlevé I and II equations to Painlevétype equations of second order and higher degree
Sakka, A. (Elsevier BV, 200207)We give Bäcklund transformations for the Painlevé I and Painlevé II equations to secondorder and higher degree equations of Painlevé type. 
B¨acklund transformations for Cosgrove’s equation FXVIII
Sakka, A. H.; Elshamy, S. (2007)In this paper we study B¨acklund transformations (BTs) for Cosgrove’s equation FXVIII.We use the generalization of Fokas and Ablowitz method to derive BTs between FXVIII and new fourthorder ordinary differential ... 
B¨acklund transformations for fourthorder Painlev´etype equations
Sakka, Ayman H.; Elshamy, Safejan R. (الجامعة الإسلامية  غزة, 2006)In this paper we study new forms of B¨acklund transformations for fourthorder ordinary differential equations of Painlev´etype. We present an algorithm which allows the construction of B¨acklund transformations between ... 
Firstorder seconddegree equations related with Painlevé equations
Sakka, A. H.; Mugan, Ugurhan (World Academic Union (World Academic Press), 2009)The firstorder seconddegree equations satisfying the Fuchs theorem concerning the absence of movable critical points, related with Painlev´e equations, and oneparameter families of solutions which solve the firstorder ... 
Lie symmetry analysis of some conformable fractional partial differential equations
Tayyan, B. A.; Sakka, A. H (Springer Science and Business Media LLC, 20181212)In this article, Lie symmetry analysis is used to investigate invariance properties of some nonlinear fractional partial differential equations with conformable fractional time and space derivatives. The analysis is ... 
Linear problems and hierarchies of Painlevé equations
Sakka, Ayman H. (IOP Publishing, 20090116)In this paper, we show that the expansion of linear problems of the Painlev´e equation in powers of the spectral variable can be used to derive hierarchies of ordinary differential equations. We applied this approach to ... 
On special solutions of second and fourth Painlevé hierarchies
Sakka, A. H. (Elsevier BV, 200902)In this article, we give special solutions of second and fourth Painlev´e hierarchies derived by Gordoa, Joshi, and Pickering. We show that for certain choice of the parameters each nth member of these hierarchies has ... 
ON TAYLOR DIFFERENTIAL TRANSFORM METHOD FOR THE FIRST PAINLEVE EQUATION
Sakka, A. H.; Sulayh, A. M. (201909)We apply the Taylor Differential Transform Method (TDTM) to the initial value problem of the fi rst Painleve equation. We use the deviation to calculate the accuracy of the solutions and the results are compared with the ... 
Schlesinger transformations for discrete second Painlevé equation: dPII
Mugan, Ugurhan; Sakka, Ayman H.; Santini, Paolo M. (2005)A method to obtain the Schlesinger transformations for the standard discrete second Painlevé equation, d–PII, is given. The procedure involves formulating a Riemann–Hilbert problem for a transformation matrix which ... 
Schlesinger transformations for Painlevé VI equation
Mugan, U.; Sakka, A. (AIP Publishing, 199503)A method to obtain the Schlesinger transformations for Painlevé VI equation is given. The procedure involves formulating a Riemann–Hilbert problem for a transformation matrix which transforms the solution of the linear ... 
Schlesinger transformations for the second members of PII and PIV hierarchies
Sakka, A H (IOP Publishing, 20070706)In this paper, we give a method to obtain the Schlesinger transformations for the second members of second and fourth Painlev´e hierarchies. The procedure involves formulating a Riemann–Hilbert problem for a transformation ... 
Secondorder fourthdegree Painlevétype equations
Sakka, A. (IOP Publishing, 20010126)Transformations that involve a Fuchsiantype equation are used to obtain onetoone correspondence between the Painlevé IIV equations and certain secondorder fourthdegree Painlevétype equations. 
SYMMETRIES AND EXACT SOLUTIONS OF CONFORMABLE FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS
Tayyan, B. A.; Sakka, A. H. (2020)In this paper Lie group analysis is used to investigate invariance properties of nonlinear fractional partial differential equations with conformable fractional time derivative. The analysis is applied to Kortewegde ... 
TRANSFORMATIONS OF PAINLEVE EQUATIONS
Sakka, Ayman H. (الجامعة الإسلامية  غزة, 2005)TRANSFORMATIONS OF PAINLEVE EQUATIONS